## This Week's Seminars and Colloquia

Monday, February 19, 2018 - 11:15 , Location: skiles 005 , Nemanja Kosovalic , University of Southern Alabama , Organizer: Livia Corsi
Using techniques from local bifurcation theory, we prove the existence of various types of temporally periodic solutions for damped wave equations, in higher dimensions. The emphasis is on understanding the role of external bifurcation parameters and symmetry, in generating the periodic motion. The work presented is joint with Brian Pigott
Monday, February 19, 2018 - 11:15 , Location: skiles 005 , Nemanja Kosovalic , University of Southern Alabama , Organizer: Livia Corsi
Using techniques from local bifurcation theory, we prove the existence of various types of temporally periodic solutions for damped wave equations, in higher dimensions. The emphasis is on understanding the role of external bifurcation parameters and symmetry, in generating the periodic motion. The work presented is joint with Brian Pigott
Monday, February 19, 2018 - 14:00 , Location: Skiles 006 , Mike Wong , LSU , Organizer: Caitlin Leverson
Although the Alexander polynomial does not satisfy an unoriented skein relation, Manolescu (2007) showed that there exists an unoriented skein exact triangle for knot Floer homology. In this talk, we will describe some developments in this direction since then, including a combinatorial proof using grid homology and extensions to the Petkova-Vertesi tangle Floer homology (joint work with Ina Petkova) and Zarev's bordered sutured Floer homology (joint work with Shea Vela-Vick).
Monday, February 19, 2018 - 14:00 , Location: Skiles 006 , Mike Wong , LSU , Organizer: Caitlin Leverson
Although the Alexander polynomial does not satisfy an unoriented skein relation, Manolescu (2007) showed that there exists an unoriented skein exact triangle for knot Floer homology. In this talk, we will describe some developments in this direction since then, including a combinatorial proof using grid homology and extensions to the Petkova-Vertesi tangle Floer homology (joint work with Ina Petkova) and Zarev's bordered sutured Floer homology (joint work with Shea Vela-Vick).
Monday, February 19, 2018 - 15:30 , Location: Skiles 005 , Greg Kuperberg , UC Davis , Organizer: Caitlin Leverson
Now that the geometrization conjecture has been proven, and the virtual Haken conjecture has been proven, what is left in 3-manifold topology? One remaining topic is the computational complexity of geometric topology problems. How difficult is it to distinguish the unknot? Or 3-manifolds from each other? The right approach to these questions is not just to consider quantitative complexity, i.e., how much work they take for a computer; but also qualitative complexity, whether there are efficient algorithms with one or another kind of help. I will discuss various results on this theme, such as that knottedness and unknottedness are both in NP; and I will discuss high-dimensional questions for context.
Monday, February 19, 2018 - 15:30 , Location: Skiles 005 , Greg Kuperberg , UC Davis , Organizer: Caitlin Leverson
Now that the geometrization conjecture has been proven, and the virtual Haken conjecture has been proven, what is left in 3-manifold topology? One remaining topic is the computational complexity of geometric topology problems. How difficult is it to distinguish the unknot? Or 3-manifolds from each other? The right approach to these questions is not just to consider quantitative complexity, i.e., how much work they take for a computer; but also qualitative complexity, whether there are efficient algorithms with one or another kind of help. I will discuss various results on this theme, such as that knottedness and unknottedness are both in NP; and I will discuss high-dimensional questions for context.
Series: PDE Seminar
Tuesday, February 20, 2018 - 15:00 , Location: Skiles 006 , , Università degli Studi di Napoli Federico II , , Organizer: Yao Yao
We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - i.e. periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. To overcome these problems, we first reduce the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme that requires very weak Melnikov non-resonance conditions (which lose derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments. This is a joint work with P. Baldi, M. Berti and R. Montalto.
Series: PDE Seminar
Tuesday, February 20, 2018 - 15:00 , Location: Skiles 006 , , Università degli Studi di Napoli Federico II , , Organizer: Yao Yao
We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - i.e. periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. To overcome these problems, we first reduce the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme that requires very weak Melnikov non-resonance conditions (which lose derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments. This is a joint work with P. Baldi, M. Berti and R. Montalto.
Wednesday, February 21, 2018 - 13:55 , Location: Skiles 005 , , Princeton University , , Organizer: Galyna Livshyts
I will speak how to dualize'' certain martingale estimates related to the dyadic square function to obtain estimates on the Hamming and vice versa. As an application of this duality approach, I will illustrate how to dualize an estimate of Davis to improve a result of Naor--Schechtman on the real line. If time allows we will consider one more example where an improvement of Beckner's estimate will be given.
Wednesday, February 21, 2018 - 13:55 , Location: Skiles 005 , , Princeton University , , Organizer: Galyna Livshyts
I will speak how to dualize'' certain martingale estimates related to the dyadic square function to obtain estimates on the Hamming and vice versa. As an application of this duality approach, I will illustrate how to dualize an estimate of Davis to improve a result of Naor--Schechtman on the real line. If time allows we will consider one more example where an improvement of Beckner's estimate will be given.
Thursday, February 22, 2018 - 11:00 , Location: Skiles 006 , , Stony Brook University , Organizer: Mayya Zhilova
A distinct covering system of congruences is a finite collection of arithmetic progressions $$a_i \bmod m_i, \qquad 1 < m_1 < m_2 < \cdots < m_k.$$Erdős asked whether the least modulus of a distinct covering system of congruences can be arbitrarily large.  I will discuss my proof that minimum modulus is at most $10^{16}$, and recent joint work with Pace Nielsen, in which it is proven that every distinct covering system of congruences has a modulus divisible by either 2 or 3.
Thursday, February 22, 2018 - 11:00 , Location: Skiles 006 , , Stony Brook University , Organizer: Mayya Zhilova
A distinct covering system of congruences is a finite collection of arithmetic progressions $$a_i \bmod m_i, \qquad 1 < m_1 < m_2 < \cdots < m_k.$$Erdős asked whether the least modulus of a distinct covering system of congruences can be arbitrarily large.  I will discuss my proof that minimum modulus is at most $10^{16}$, and recent joint work with Pace Nielsen, in which it is proven that every distinct covering system of congruences has a modulus divisible by either 2 or 3.
Friday, February 23, 2018 - 10:00 , Location: Skiles 006 , , Georgia Tech , , Organizer: Kisun Lee
TBA
Friday, February 23, 2018 - 10:00 , Location: Skiles 006 , , Georgia Tech , , Organizer: Kisun Lee
TBA
Friday, February 23, 2018 - 10:00 , Location: Skiles 006 , , Georgia Tech , , Organizer: Kisun Lee
TBA
Friday, February 23, 2018 - 10:00 , Location: Skiles 006 , , Georgia Tech , , Organizer: Kisun Lee
TBA
Friday, February 23, 2018 - 13:55 , Location: Skiles 269 , , Morehouse University , Organizer: Sung Ha Kang
We use a stochastic dynamic programming approach to address the following question: Can a homogenous resource extraction model (one without extraction costs, without new discoveries, and without technical progress) generate non-increasing resource prices?  The traditional answer to that question contends that prices should exhibit an increasing trend as the exhaustible resource is being depleted over time (The Hotelling rule). In contrast, we will show that injecting concerns for temporal resolution of uncertainty in a resource extraction problem can generate a non-increasing trend in the resource price.  Indeed, the expected rate of change of the price can become negative if the premium for temporal resolution of uncertainty is negative and outweighs both the positive discount rate and the short-run risk premium.  Numerical examples are provided for illustration.
Friday, February 23, 2018 - 13:55 , Location: Skiles 269 , , Morehouse University , Organizer: Sung Ha Kang
We use a stochastic dynamic programming approach to address the following question: Can a homogenous resource extraction model (one without extraction costs, without new discoveries, and without technical progress) generate non-increasing resource prices?  The traditional answer to that question contends that prices should exhibit an increasing trend as the exhaustible resource is being depleted over time (The Hotelling rule). In contrast, we will show that injecting concerns for temporal resolution of uncertainty in a resource extraction problem can generate a non-increasing trend in the resource price.  Indeed, the expected rate of change of the price can become negative if the premium for temporal resolution of uncertainty is negative and outweighs both the positive discount rate and the short-run risk premium.  Numerical examples are provided for illustration.
Friday, February 23, 2018 - 14:00 , Location: none , none , none , Organizer: John Etnyre
Friday, February 23, 2018 - 14:00 , Location: none , none , none , Organizer: John Etnyre
Friday, February 23, 2018 - 15:00 , Location: Skiles 271 , Jiaqi Yang , GT Math , Organizer: Jiaqi Yang
We will present a rigorous proof of non-existence of homotopically non-trivial invariant circles for standard map:x_{n+1}=x_n+y_{n+1}; y_{n+1}=y_n+\frac{k}{2\pi}\sin(2\pi x_n).This a work by J. Mather in 1984.
Friday, February 23, 2018 - 15:00 , Location: Skiles 271 , Jiaqi Yang , GT Math , Organizer: Jiaqi Yang
We will present a rigorous proof of non-existence of homotopically non-trivial invariant circles for standard map:x_{n+1}=x_n+y_{n+1}; y_{n+1}=y_n+\frac{k}{2\pi}\sin(2\pi x_n).This a work by J. Mather in 1984.
Friday, February 23, 2018 - 15:05 , Location: Skiles 005 , Robert Hough , SUNY, Stony Brook , , Organizer: Prasad Tetali
I will describe two new local limit theorems on the Heisenberg group, and on an arbitrary connected, simply connected nilpotent Lie group.  The limit theorems admit general driving measures and permit testing against test functions with an arbitrary translation on the left and the right. The techniques introduced include a rearrangement group action, the Gowers-Cauchy-Schwarz inequality, and a Lindeberg replacement scheme which approximates the driving measure with the corresponding heat kernel.  These results generalize earlier local limit theorems of Alexopoulos and Breuillard, answering several open questions.  The work on the Heisenberg group is joint with Persi Diaconis.
Friday, February 23, 2018 - 15:05 , Location: Skiles 005 , Robert Hough , SUNY, Stony Brook , , Organizer: Prasad Tetali
I will describe two new local limit theorems on the Heisenberg group, and on an arbitrary connected, simply connected nilpotent Lie group.  The limit theorems admit general driving measures and permit testing against test functions with an arbitrary translation on the left and the right. The techniques introduced include a rearrangement group action, the Gowers-Cauchy-Schwarz inequality, and a Lindeberg replacement scheme which approximates the driving measure with the corresponding heat kernel.  These results generalize earlier local limit theorems of Alexopoulos and Breuillard, answering several open questions.  The work on the Heisenberg group is joint with Persi Diaconis.
Series: Other Talks
Friday, February 23, 2018 - 17:00 , Location: Classroom 105 in the D.M. Smith building , , Swarthmore College , Organizer: Joseph Rabinoff
Degeneracy loci of morphisms between vector bundles have been used in a wide range of situations, including classical approaches to the Brill--Noether theory of special divisors on curves. I will describe recent developments in Schubert calculus, including K-theoretic formulas for degeneracy loci and their applications to K-classes of Brill--Noether loci. These recover the formulas of Eisenbud--Harris, Pirola, and Chan--López--Pflueger--Teixidor for Brill--Noether curves. This is joint work with Dave Anderson and Nicola Tarasca.
Series: Other Talks
Friday, February 23, 2018 - 17:00 , Location: Classroom 105 in the D.M. Smith building , , Swarthmore College , Organizer: Joseph Rabinoff
Degeneracy loci of morphisms between vector bundles have been used in a wide range of situations, including classical approaches to the Brill--Noether theory of special divisors on curves. I will describe recent developments in Schubert calculus, including K-theoretic formulas for degeneracy loci and their applications to K-classes of Brill--Noether loci. These recover the formulas of Eisenbud--Harris, Pirola, and Chan--López--Pflueger--Teixidor for Brill--Noether curves. This is joint work with Dave Anderson and Nicola Tarasca.
Saturday, February 24, 2018 - 09:30 , Location: Helen M. Aderhold Learning Center (ALC), Room 24 (60 Luckie St NW, Atlanta, GA 30303) , Wenjing Liao and others , GSU, Clemson,UGA, GT, Emory , Organizer: Sung Ha Kang
The Georgia Scientific Computing Symposium is a forum for professors, postdocs, graduate students and other researchers in Georgia to meet in an informal setting, to exchange ideas, and to highlight local scientific computing research. The symposium has been held every year since 2009 and is open to the entire research community. This year, the symposium will be held on Saturday, February 24, 2018, at Georgia State University. More information can be found at: https://math.gsu.edu/xye/public/gscs/gscs2018.html
Saturday, February 24, 2018 - 09:30 , Location: Helen M. Aderhold Learning Center (ALC), Room 24 (60 Luckie St NW, Atlanta, GA 30303) , Wenjing Liao and others , GSU, Clemson,UGA, GT, Emory , Organizer: Sung Ha Kang
The Georgia Scientific Computing Symposium is a forum for professors, postdocs, graduate students and other researchers in Georgia to meet in an informal setting, to exchange ideas, and to highlight local scientific computing research. The symposium has been held every year since 2009 and is open to the entire research community. This year, the symposium will be held on Saturday, February 24, 2018, at Georgia State University. More information can be found at: https://math.gsu.edu/xye/public/gscs/gscs2018.html